Abstract: This paper proposes a Multi-Stage FastICA Algorithm(MSFICA) to solve the problem of error propagation in the traditional successive FastICA algorithm. MSFICA removes the error propagation effect through a two-stage structure. In order to reduce the computational complexity, a dimension decrease method is used to get the initial values of separating vectors in the first stage. In the second stage, the algorithm uses the initial values and whitened observed signals to separate original signals, and does not need orthogonal projection. Simulation results indicate that the proposed algorithm can eliminate error propagation successfully and achieve better performance than existing parallel FastICA algorithm at the expense of a slightly increased complexity.